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Truncated Power-Normal Distribution with Application to Non-Negative Measurements.

Nabor O Castillo1, Diego I Gallardo2, Heleno Bolfarine3

  • 1Departamento de Matemáticas, Facultad de Ciencias, Universidad de La Serena, La Serena 1700000, Chile.

Entropy (Basel, Switzerland)
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Summary
This summary is machine-generated.

This study introduces a new truncated power-normal distribution for positive data. The proposed model shows good performance when compared to existing distributions for real-world datasets.

Keywords:
Shannon entropymaximum likelihoodpower-normal distributiontruncation

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Area of Science:

  • Statistics
  • Probability Theory
  • Mathematical Statistics

Background:

  • The power-normal (PN) distribution is a flexible model for continuous data.
  • Existing models may not adequately capture the characteristics of positive-valued data.
  • Truncated distributions offer a way to adapt existing models for specific data ranges.

Purpose of the Study:

  • To introduce and study a truncated positive version of the power-normal distribution.
  • To extend the half-normal distribution by using a zero truncation point.
  • To evaluate the proposed model's performance for positive data.

Main Methods:

  • Derivation of probabilistic properties for the new distribution.
  • Estimation of model parameters using maximum likelihood and moments methods.
  • Fitting the proposed model to two real-world positive datasets.

Main Results:

  • The proposed truncated power-normal model demonstrates good performance.
  • The model serves as a viable extension of the half-normal distribution.
  • Comparative analysis indicates favorable results against alternative models for positive data.

Conclusions:

  • The truncated positive power-normal distribution is a promising model for analyzing positive data.
  • The estimation methods (maximum likelihood and moments) are effective for the proposed model.
  • The model's flexibility and performance make it suitable for practical applications in statistics.